Only if you have very limited expectations for Web surfing. Computers more than a few years old are going to have a hard time with YouTube, and with a lot of Flash pages.
The Web has shifted the definition of obsolescence; it's true that whatever a computer can do the day you buy it, it will continue to do for years and years; but long before the hardware fails, "doing the same stuff" will no longer include visiting the same Web sites.
I kind of disagree. At this point Flash really hasn’t done anything for 6 years except for upgrade small bits here and there, heck they still haven’t released a 64bit version for Vista or Windows 7. On another note CPU technology is starting to get stale a bit. While the Phenom II and C2D offer a fairly decent boost in performance in some areas, in others like internet browsing they offer no real boost to old first gen dual cores like the Athlon64 Dual Cores or even the single core Athlon 64. Which I can personally attest too, having 3 different generation cpu’s at my house. One is the internet machine which has the 5 year old Athlon 64, another a newer Phenom 4 core and another(my laptop) has a C2D and for internet use and word documents I notice no real difference in usage, at times even my single core actually outperforms both because I have more ram(4GB) than the other two which has three. Now if we are talking databases like Access or games, the newer the better, especially with the very large databases, which would want a fast cpu to peruse very large db’s) or newer games which of course rely on better hardware all around.